Question

shakira invests $500000 at 5% compound intwerest per annum . calculate how many years it takes for the value to double in value?

Answer 1

~14.2066 years

Explanation:

assuming p.a. means per annual:

$500,000 with intrest rate 5% per year. how many years for money to become $1,000,000?

with annual intrest, a percentage of the money you invest is added to your balance every year

set up equation: (original money*(1+ intrest rate))^x=goal money

there is a 1 because you are adding on to the original (100%) amount of money

x is the number of years untill goal money. is an exponent because it depends on the previous years balance. note that amount of money gained will change per year.

50,000*(1+0.05)^x=1,000,000

solve------

divide by 50,000 both sides

1*(1+0.05)^x=2

(1+0.05)^x=2

(1.05)^x=2

apply log_1.05 to both sides

log_1.05 (1.05)^x= log_1.05 2

x= log_1.05 2

use calculator to approx

~14.2067 years

hope this helps

Answer 2

`t=14.2\ years`

Explanation:

we know that

The compound interest formula is equal to

`A=P(1+(r)/(n))^(nt)`

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

`t=?\ years\\ P=\$500,000\\ r=0.05\\n=1\\ A=\$1,000,000`

substitute in the formula above and solve for t

`1,000,000=500,000(1+(0.05)/(1))^((1)t)`

`2=(1.05})^(t)`

Apply log both sides

`log(2)=log[(1.05})^(t)]`

`log(2)=(t)log(1.05)`

`t=log(2)/log(1.05)`

`t=14.2\ years`